Design of the Traction Battery fora Formula SAE Racing Car

Federico Baronti⇤, Daniele Calderini§, Gianluca Caposciutti§, Andrea Gassani§ Riccardo Moras§ and Roberto Saletti⇤⇤Dipartimento di Ingegneria dell’Informazione, Universita di Pisa, I-56122 Pisa, Italy E-mail: f.baronti@iet.unipi.it

§E-Team Squadra Corse, Universita di Pisa, I-56122 Pisa, Italy

Abstract—This paper describes the design of the traction

battery for the new electric Formula SAE vehicle of the University

of Pisa. A model based design methodology extended to the

mechanical, electrical and thermal domains was applied to find

the best trade-off between the battery weight and the maximum

power available at the wheel. The designed battery configuration

was validated by means of electrical and thermal simulations.

I. INTRODUCTION

Formula SAE (FSAE) is an international racing competi-tion created by the Society of Automotive Engineers in 1978.It is held every year in several locations around the world andchallenges university students. They are asked to conceive,design and drive a small, formula style vehicle complyingwith the official FSAE rules [1]. With the growing interest forsustainable transportation, this competition, originally reservedfor combustion engine vehicles, was extended to electric onesin 2010, in order to foster education and research on electricmobility [2]–[4]. Each round of the competition consists ofstatic and dynamic events. During the former, students presentand discuss their design choices with experts from academyand industry. Both technical and economical aspects are evalu-ated with the view to a small series production of the designedvehicle. Dynamic events include an acceleration test and anendurance race of approximately 20 km.

The onboard energy storage system (ESS) dramaticallyaffects the dynamic performance of an electric FSAE car, asthe ESS weight is a significant portion of the overall vehicleweight. Thus, its optimization under the constraint that theESS provides the high power requested during the accelerationtest and stores enough energy to complete the endurance race,is a fundamental design goal for an electric FSAE car. Thisgoal can be achieved by using the Lithium Polymer (LiPo)battery technology, which provides a very good trade-offbetween power and energy densities, compared to other ESStechnologies [5]. However, this battery technology is famousfor its fragility, as it cannot withstand operation outside welldefined voltage and temperature ranges. The traction batteryof a FSAE electric car has to be as light as possible andprovide suitable acceleration capabilities. Thus, it is subjectedto high C-rate discharging currents, which are likely to createthermal problems if the mechanical assembly of the batterycells, as well as the cooling system, are not properly designedand validated.

The objective of this paper is to describe the methodologyused to size, design and validate the traction battery of theFSAE racing car, which is being developed at the University

of Pisa (Italy). An important point of this work is the adoptionof a model-based design approach that integrates all theengineering fields involved in the application, i.e., mechanical,electrical and thermal fields. In fact, the optimum sizing ofthe battery was obtained by means of a dynamic model of theFSAE car running an endurance race. The correct behavior ofthe battery was then verified by electrical simulations, whichexploit an accurate model of LiPo cells. Finally, a thermalmodel of the battery cells considering the designed mechanicallayout and the cooling system was developed and Compu-tational Fluid Dynamics (CFD) analyses were performed toverify that the cell temperatures remain in the safe range duringthe endurance race.

II. BATTERY DESIGN

The exploration of the design space of the ESS is boundedby the relevant FSAE Rules [1]. Their purpose is to guaranteethe safety of the students during the car assembly and thedynamic events. In the following, we report the most importantconstraints that apply to the design of the ESS for a FSAEracing car [1].

• All types of accumulators except molten salt andthermal batteries are allowed. E.g.: Batteries, Super-capacitors, etc. Fuel cells are prohibited.

• The maximum permitted voltage is 600 V.

• Each battery segment must contain a maximum energyof 12 MJ and its static voltage must be less than 120 V.

• The maximum power drawn from the battery must notexceed 85 kW.

• A Battery Management System (BMS) is mandatoryto continuously measure the voltage of every cell andthe temperature of at least 30 % of the cells.

A. Battery Sizing

A state of the art analysis of other FSAE electric carswas carried out as a starting point for the exploration of theESS design space. This analysis pointed out that the LiPobattery technology is the common choice of the FSAE topteams for the implementation of the onboard ESS. Comparedto other ESS technologies, LiPo battery cells provide indeeda very good trade-off between power and energy densities,at the expense of a higher sensitivity to overcharge, deepdischarge and overtemperature [5]. As the weight of the ESShas a significant impact on the performance of the vehicle,

Fig. 1. Flow diagram of the battery size optmization.

we selected this battery technology, though it poses severechallenges on its electrical and thermal management that haveto be properly faced.

The preliminary step for designing the ESS was to deter-mine the battery energy size E

B

needed to complete the race,which minimizes the lap time. On the one hand, decreasingE

B

and consequently the vehicle mass MV

(which includesthe ESS mass) makes the car faster when cornering. On theother hand, it requires a reduction of the maximum powerat the wheels P

W

(to complete the race), which makes thecar slower when going straight. Thus, we expect the existenceof an optimum value of E

B

. To find this value, a simplebut accurate simulation environment was developed using theMathematicar software. It is based on a simple point massmodel of the vehicle, which is assumed to follow an assignedpath, driven by an ideal driver. The ideal driver imposes theoptimal speed profile, computed considering M

V

, PW

, theaerodynamics forces and the tires characteristics. The powerat the battery terminals is obtained considering the inverterefficiency and the electric motor efficiency map. The modelwas used to simulate the endurance race on the circuit of theFormula Student Germany, whose track layout and parametershave been extracted from the data logged during the FSAEevent in 2011 [6]. The outputs of the simulation are the energyused to complete the race E

race

and the time needed to travelone lap of the track T

lap

, as well as the power at the batteryterminals.

The optimization procedure consisted in varying PW

from26 kW to 40 kW and in finding for each P

W

value, thecorresponding value of E

B

that guarantees to complete the racewith a desired safety margin. As E

race

depends on the vehiclemass, which in turn depends on E

B

, the iterative algorithmdescribed in (1) was used to obtain E

B

for each analyzedvalue of P

W

, as shown in the flow diagram of Fig. 1. The“Simulate Point Mass Model” block receives P

W

and MV

asinput and the vehicle and track data as parameters. P

W

is setat the beginning of the procedure, whereas M

V

is updated ateach iteration by the “Update Vehicle Mass”. The procedureends when the absolute difference between two consecutivevalues of E

race

is less than 100W h. The vehicle mass is thesum of a constant term M

C

, which includes all the onboardmasses except the ESS, and the ESS itself. The experience of

26 28 30 32 34 36 38 405.5

6

6.5

7

7.5

Batte

ry S

ize

(kW

h)

26 28 30 32 34 36 38 4044.3

44.4

44.5

44.6

44.7

Maximum Power at Wheels (kW)

Lap

Tim

e (s

)

Battery SizeLap Time

Fig. 2. Battery size and lap time as function of the maximum power at thewheels.

the previous FSAE cars leads to an estimate of MC

= 200 kg[6]. The ESS mass is computed by dividing E

B

by the ESSenergy density ⇢

B

. We assumed ⇢B

= 100W h kg�1, which isa reasonable value for the LiPo battery technology consideringthe overhead due to the assembling of the battery pack. Thenext value of E

B

is obtained as the simulation result Erace

times a factor k, with k > 1, which determines the amount ofresidual energy stored in the battery at the end of the race. Bysetting k = 1.1, we avoid the deep discharge of the batteryas its state of charge at the end of the endurance event is still10%.

8<

:

EB

(0) = 7 kW hE

B

(i) = kErace

(i� 1)

MV

= MC

+ EB

(i)/⇢B

(1)

Figure 2 shows the battery size EB

and the lap timeTlap

, as a function of PW

. The lap time is minimized withPW

= 34.4 kW, which yields Tlap

= 44.33 s and EB

=6.8 kW h. This battery size is in good agreement with thosefound in the survey of other electric FSAE cars, which lie inthe range 5 kW h to 7 kW h. Figure 2 also shows that decreasingPW

down to 26 kW, the lap time increases of less than 1%and the required stored energy E

B

is reduced to 5.8 kW h.This introduces a valuable flexibility, which can be exploitedin completing the design of the battery. To this end, giventhe number of series-connected cells N , the nominal voltageVn

= 3.7V of a LiPo cell, the cell capacity Cn

, we express EB

as in (2). It is useful to relate EB

to the maximum voltage atthe battery’s terminals V

max

= 4.2N , being 4.2V the voltageof a fully charged LiPo cell. As V

max

is limited by the FSAErules to 600V, the maximum number of LiPo cells that canbe serially connected is 142. In this configuration, the cellcapacity to store the optimum amount of energy 7 kW h is12.9A h.

EB

= NVn

Cn

=3.7

4.2Vmax

Cn

(2)

For the selection of the battery cell, we also need to esti-mate the maximum discharging continuous and peak powersof the battery. The maximum discharging power is requiredduring the acceleration event, in which the maximum allowed(by FSAE rules) power P

B,peak = 85 kW is requested fromthe battery for a short time (less than 10 s). As P

W

waslimited in our design exploration to 40 kW, we end up to a

(a) (b) (c)

Fig. 3. (a) Cells series-connection detail. (b) Segment configuration. (c) BMS slave boards connection.

0 5 10 15 20 25 30 35 40 45

−10

0

10

20

30

Time (s)

Pow

er (k

W)

Power@Wheels Power@Battery

Fig. 4. Power at wheels and at the battery’s terminals during one lap.

maximum “continuous” discharging power PB,cont ' 45 kW,

taking into account all the energy losses from the battery towheels (i.e., approximately an 88% efficiency from the batteryto the wheels). From E

B

and the continuous and peak valuesof the maximum discharge power, it is possible to estimate thecontinuous and peak values of the maximum discharge currentin terms of C-rate, Crate

cont

and Cratepeak

, respectively.

PB,cont = NV

n

Cn

1 hCrate

cont

=E

B

1 hCrate

cont

PB,peak = NV

n

Cn

1 hCrate

peak

=E

B

1 hCrate

peak

(3)

From (3), we obtain Cratecont

⇡ 7 and Cratepeak

⇡ 13,values that must be sustained by the cell to be selected. Thismeans that high power cells are needed, thus, confirmingthe initial choice of the LiPo battery technology. A verygood trade-off between power and energy densities is indeedfound in the 12A h LiPo cell (SLPB70205130P) from KokamUltra-High-Power Series. The maximum continuous and peakdischarge (for less than 20 s) currents are 15 and 20 C-rate, respectively, and the mass is 350 g, thus satisfying thepreviously stated requirements. The cell case is the pouch type.

B. Battery assembly

To complete the design of the traction battery, we have todecide how to assemble the selected elemental cells to storethe required energy with the constraints imposed by the FSAE

rules. We chose to partition the battery into 6 segments of23 cells each. The overall number of series-connected 12A hcells is 138, which leads to a maximum voltage of 579.6Vand a stored energy of 6127.2W h. According to Fig. 2, themaximum power at wheels is thus limited to 29 kW. This leadsto T

lap

= 44.47 s, which is very close to the minimum value.Each segment has a maximum voltage of 96.6V and storesapproximately 3.7MJ, thus complying with the FSAE rules.

Figure 3 shows the designed assembly of a segment. Inparticular, Fig. 3(a) shows the connection between adjacentcells, which is obtained by folding the tabs of two adjacentcells and assuring the electrical connection by pressing themagainst an insulating substrate by means of an aluminumtab. The shape of the latter is designed so that it can becontacted from a an overlaid board (see Fig. 3(b)), whichhosts the slave boards of the BMS. The adopted BMS hasindeed a hierarchical architecture, in which the voltage andtemperature of each cell are measured by a dedicated slaveboard. The slave board are chained and eventually connectedto the master BMS unit. This assembly provides a reliableelectrical connection between the serially connected cells anda simple and effective connection to the BMS. The goal is areduction of the production costs in a serial production of thevehicle, which is positively evaluated by the FSAE judges.

The overall mass of the designed battery is estimated tobe around 65 kg. This is in good agreement with the initialhypothesis on the energy density ⇢

B

= 100W h kg�1 andE

B

= 6.1 kW h. Finally, Fig. 4 shows the power at the battery’sterminals (for P

W

= 29 kW) during one lap of the race, whichis used for the electrical and thermal simulations described inthe following Sections.

III. ELECTRICAL SIMULATIONS

The process described above allowed us to design thebattery configuration that satisfies the requirements of thetarget application in terms of power and energy. The main issueis now to verify that, during the endurance event, the batteryremains in the safe operating area, in terms of the voltageand temperature of the cells, while providing the requestedpower. This issue has been addressed by electrical and thermalsimulations. The former exploits an accurate model of LiPocells developed in [7], which is capable of reproducing thedynamic behavior of the cell voltage faithfully, given the cellcurrent. Thermal simulations are based on a CFD model of

Fig. 5. Electrical model of a LiPo cell.

BMS

Charge Error

Current_In

Current_Out SoC

Cell Voltage

Vin+

Vin-

CellSoC

V+ V-

Signal_current

V

Voltage_sensor

Division

k=138

Cells_number

Power

Delay

Ground

Fig. 6. Block diagram of the model used for the electrical simulations inDymola.

the battery, which takes into account the battery assemblygeometry, as well as the cooling system. The heat generatedin the battery is due to the power dissipated by the cells, asobtained by the electrical simulations.

A. Electrical Model

Figure 5 shows an equivalent electrical model of a cellwidely accepted in the literature [8]. The left hand side ofthe model in Fig. 5 reproduces the State-of-Charge (SoC) ofthe cell by means of Coulomb-counting of the cell current i.The right hand side reproduces the cell terminal voltage v, asa sum of the Open Circuit Voltage (OCV), which is a nonlinear function of the SoC, and two relaxation voltages v

RC1

and vRC2

. The corresponding time constants are in the orderof tens and hundreds of seconds, respectively [9]. The modelparameters are not constant as they depend on the SoC and thetemperature of the cell and are managed by a 2-dimensionalLook-Up-Table (LUT). The relationship between OCV andSoC is also recorded in a LUT.

The electrical model shown in Fig. 5 was fully character-ized for a 1.5A h cell belonging to same family of the cellsused in the battery described in this work [7]. We note thata 12A h cell can be modeled by the parallel of 8 cells of thesame chemistry with a capacity of 1.5A h. Thus, the modelparameters related to the 12A h were obtained by scalinga factor 8 those of the 1.5A h, i.e., dividing the resistiveterms and multiplying the capacitive ones. The SoC-OCVrelationship depends only on the battery chemistry and isinvariant with the cell capacity.

B. Electrical Simulations

The electrical model was implemented in the Dymolasimulator, a multi-domain simulation software. Only one cellof the battery is simulated as all the cells are identical and

-40

-20

0

20

40

60

80

100

Ce

ll C

urr

en

t (A

)

0.0

0.2

0.4

0.6

0.8

1.0

Ce

ll S

tate

-of-

Ch

arg

e

0.0

0.2

0.4

0.6

0.8

1.0

Ce

ll S

tate

-of-

Ch

arg

e

2.0

2.5

3.0

3.5

4.0

4.5

0 200 400 600 800 1000 1200 1400C

ell

Vo

ltag

e (

V)

Time (s)

2.0

2.5

3.0

3.5

4.0

4.5

0 200 400 600 800 1000 1200 1400C

ell

Vo

ltag

e (

V)

Time (s)

Fig. 7. Cell current, SoC and voltage during the endurance race supposinga maximum power of 29 kW available at the wheels. The red lines show thesafety limits.

are subjected to the same current. Thus, the voltage of thebattery is 138 time that of a single cell. The block diagramof the simulation set-up is shown in Fig. 6. It includes the“Cell” block that accounts for the right hand side of theelectrical model shown in Fig. 5. Its left hand side is insteadincorporated in the “BMS” block, which also controls that thevoltage and current of the cell remain in their proper saferanges. The input of the simulation is the battery power profileshown in Fig. 4, which is repeated for all the 28 laps ofthe endurance race. The battery current is computed at eachsimulation step by dividing the current input power by thebattery voltage computed at the previous simulation step.

The behavior of the cell voltage during the endurance raceis shown in the bottom chart of Fig. 7. It is worth noting thatthe cell voltage always remains above the discharge cut-offvoltage (red line), which is specified by the producer as 2.7V.Also, the battery SoC at the end of the endurance race is around10%, as expected from the analysis carried out in Section II-Ato size the battery. The top chart of Fig. 7 shows the batterycurrent that increases to maintain the same power profile lapafter lap when the battery voltage decreases. From the batterycurrent, we calculated the power losses in each cell as thepower dissipated by the resistor R

0

in the electrical modelof Fig. 5. For this computation, we considered R

0

constantand equal to 2.2 m⌦. These losses are the bridge to the nextthermal domain analysis.

IV. THERMAL SIMULATIONS

The objective of this section is to verify that each cell ofthe battery remains below 55 �C, a safe temperature for theused battery technology, during all the endurance race. To this

Fig. 8. Simplified 3D view of the battery assembly. The cell analyzed is thatin dark grey.

end, we developed a thermal model of the whole battery, whichaccounts for the physical assembly of the six battery segments(see Fig. 3(c)) and the cooling system. The six segments arearranged in two rows (3x23 cells per row) inside a carbon-fiber-reinforced polymer case, which is located under the pilotseat. Fig. 8 shows the battery layout, together with the coolingmechanism. The latter is based on four cooling air channels:one in the middle of the case, two on the outer sides and onebelow the cells. The air inlet is located in the upper part ofthe case above the middle and lateral channels and the outlet(a 30x7 mm2 hole) is placed under every cell. In this way, theair flux is in countercurrent with natural convection to promoteflow turbulence. The air flux is distributed by small fans, whichare sized to have approximately 5⇥ 10�4 kg s�1 cooling airfor every cell.

The key point in developing the thermal model is findingthe right trade-off between accuracy in predicting the max-imum cell temperature over the endurance race and compu-tational complexity. Two considerations can be derived fromthe physical layout of the battery. First, the most criticalcells are those located in the middle of the case. Second,the system is symmetric about the yz plane, which lies inthe center of the middle air channel, whose width is twicethat of the side channels (see Fig. 9). Thus, we can simplifythe problem by considering only the cell located in the centerof a row. Moreover, we assume that heat exchange occursonly between the lateral and bottom walls of the cell and thecorresponding air channels, while all the other surfaces areconsidered adiabatic, as shown in Fig. 9. Thermal generationwithin the cell is assumed to be uniformly distributed in spaceand is computed as the power losses in a cell divided by itsvolume, i.e., 210x132x7.5 mm3 (width x height x thickness).The thermal parameters of the cell are reported in Table I [10].Finally, we note that all the assumptions made in developingthe thermal model lead to overestimate the maximum celltemperature. Thus, if the simulated maximum cell temperatureis below the safe one, we can expect that all the battery cellsremain safely below the maximum permitted temperature.

Thermal simulations were carried out with the ANSYSFLUENT v14.0 software. The cell temperature behavior wassimulated for a a complete endurance race, which lasts around1245 s. The initial condition is the cell in the equilibrium with

Fig. 9. Schematic representation of the used thermal model.

TABLE I. THERMAL PARAMETERS OF A LITHIUM-ION CELL

Parameter Unit Typical range Used value

Thermal conductivity W/(m K) 0.40 - 0.85 0.66Specific heat at constant pressure J/(kg K) 650 - 950 800Density kg/m3 1700 - 2500 2100

the air at 35 �C, a reasonable value near the asphalt in summer.The temperature map at the end of the endurance race in themiddle section (parallel to the xy plane) of the simulated cellis shown in Fig. 10. As expected, the highest temperature isin the center-top of the cell, but safely below the maximumvalue of 55 �C.

With a convergence analysis based on successive meshrefinements, we estimated a maximum temperature error ofabout 1 �C. To validate the CFD solution, we computed theanalytical solution of the thermal problem in the middlesection (parallel to the xy plane) of the cell. To this end, weused the cell thermal parameters reported in Table I and wemodeled the heat transfer at the cell boundaries with constantcoefficients calculated for rectangular plates [11]. The thermalgeneration function was approximated by its average value,plus a sinusoidal component extracted from its Fourier series.This approximation made it possible to apply the Green’stechnique [12]. The analytical solution computed within thecell is compared to the CFD one in Fig. 11. The figure shows agood agreement between the two solutions, in particular in the

Fig. 10. Temperature map at the end of the endurance race in the middlesection (parallel to the xy plane) of the simulated cell.

30

35

40

45

50

55

60

0 40 80 120 160 200 240

Ce

ll te

mp

era

ture

(°C

)

x (mm)

Analytical

CFD

Fig. 11. Cell temperature variation along the x-axis at the end of theendurance race.

30

35

40

45

50

55

60

0 200 400 600 800 1000 1200 1400

Ce

ll te

mp

era

ture

(°C

)

Time (s)

Fig. 12. Temperature in the center of cell during the endurance race.

center of the cell, where the approximations made to calculatethe analytical solution on the boundary heat transfer are lessrelevant. Both solutions agree that the maximum temperaturepresent in the center of the cell is about 51 �C, a value safelybelow the maximum permitted.

Finally, Fig. 12 shows the cell temperature behavior duringthe endurance race. It confirms that the cell temperature atthe end of the endurance race does not exceed the maximumpermitted value, also including computational errors, startingfrom an initial temperature of 35 �C. In fact, the net resultof the thermal simulations is that the cell temperature raisesof 16 �C during the race. We note that the final value ofthe cell temperature can be adjusted by controlling the initialtemperature of the battery, a technique permitted by the FSAErules.

V. CONCLUSION

This paper has described the design of a Lithium-ionbattery to be used as energy storage for the electrical propul-sion of a FSAE electric race car. The main specificationsof the battery have been determined starting from the FSAErules. Then, LiPo high-power cells have properly been chosenaccording to the power and energy needed by the application.These requirements have been obtained with an optimizationprocedure based on a dynamic model of the vehicle. Thetwo fundamental issues related to the electrical and thermalbehavior of the battery have been addressed with electrical

and thermal simulations that take into account the power loadprofile of the battery calculated with the dynamic model ofthe vehicle. The simulations demonstrate that the endurancerace can be completed without safety risks and even withoutimpairing the health of the battery, which remains above 10%of SoC and do not enter the deep discharge region, if themaximum mechanical power is limited to 29 kW. In this casethe cooling system maintains the most critical cell maximumtemperature below the limit of 55 �C.

The final conclusion is that the design of a battery systemfor a demanding application such as the FSAE electric racecars can efficiently be solved with an effective integrationof multi-disciplines competences and multi-dimensional mod-eling that spans over the mechanical, electrical and thermalaspects of the system. Up-to-date simulation tools are alsoneeded to validate the design choices before prototyping thebattery system.

ACKNOWLEDGMENT

The authors would like to acknowledge Dr. FrancescoBucchi, Prof. Massimo Ceraolo, Dr. Gabriele Fantechi, andProf. Massimo Guiggiani for their valuable contribution to thiswork.

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